Match analysis and probability of winning a point in elite men’s singles tennis

Notational analysis and new technologies have allowed a better understanding of tactical actions in tennis. In particular, the combined analysis of different variables affecting performance is necessary to understand the relationships between actions in competition. The aim of this research was to analyse the probability of winning a point in men’s professional tennis based on the most relevant variables affecting performance in this sport. A total of 4,669 points were analysed on three different court surfaces from the final rounds (from the quarter-finals onwards) of three of the four Grand Slam tournaments in the 2021 season. An observational methodology was applied. Different analysis techniques were used to obtain the results: descriptive and chi-square with a significance level of p<0.05. First serve effectiveness (point won) was 69% on clay, 75% on grass and 75% on hard court. Second serve effectiveness (point won) was around 55% regardless of the surface. The majority of points, between 65% and 77% depending on the court surface, ended with a short rally (between one and four shots). Approximately 80% of the points played with first serve and short rally were won by the serving player. With first serve and medium length rallies, the probability of winning the point is similar between server (range 49–55%) and receiver on any court surface. The study reveals a set of patterns (based on the combination of information from the variables analysed) that determine the probability of winning a point. Descriptive data from this research could help coaches and players on match strategy at the highest levels of elite men’s single tennis.

sure it is accurate.

Unfunded studies
Enter: The author(s) received no specific funding for this work.Yes -all data are fully available without restriction

Introduction
Match analysis in tennis is a topic of interest to sport performance researchers, as can be seen in the numerous investigations that have proliferated recently [1][2][3][4].Until the last decade, tennis has not been a sport where notational analysis data has been used for performance improvement, although this has been changing in recent years [1,5].
The introduction of new technologies in this sport is generating a large amount of data on the analysis of the competition.It is now possible to access statistical information of different kinds without difficulty.The Association of Tennis Professionals (ATP), the Women's Tennis Association (WTA) and the International Tennis Federation (ITF) provide statistics on the most relevant competitions through their partnerships with Infosys, SAP and Slam Tracker [6].This data can help tennis players' teams to optimise training and improve performance in competition.It can also be useful to prepare match strategies and help decision making during the match [5,7].
New analytical techniques have optimised the interpretation of sport data and have led to more meaningful knowledge [8].One of the most recently employed techniques in sport sciences are predictive models based on tree diagrams, which have proven to be very useful for detecting behavioural patterns in team sports [9], wrestling sports [10,11] and also in racket sports [2], although in the latter case it has not been widely used so far.This data analysis incorporates the so-called performance indicators, which are those variables that have the greatest influence on the final result of the match.
The scientific literature in tennis has corroborated that a fundamental element for the optimisation of results is the ability to decide with which type of stroke, speed or spin to hit the ball at each moment of the match [12], although it also depends on other factors such as weather conditions, the opponent or the type of tournament or round [13,14].what about court surface, tournament round,, etc?
In any case, most researchers agree that the serve is the most decisive technical action of the game [3], due to the fact that the server grants the first opportunity to get the point through an ace, an error by the opponent or to obtain a tactical superiority that puts him/her in an advantageous situation during the first shots [12], where it has been shown that most of the points are finished [15].Another key factor in the match is the type of surface on which the game is played.The ITF classification divides court surfaces into 5 categories (slow, medium slow, medium, medium fast and fast).In the case of slow surfaces (e.g.: clay), the ball will present a higher coefficient of friction, a decreased horizontal speed and an increased bounce height; in the case of fast surfaces (e.g.: grass or hard track) the opposite will be happening [16].
These surfaces change with respect to the tournament [17] and cause points to develop faster or slower [18].This aspect influences another key performance indicator in the sport: rally length.Researchers have corroborated that most rallies end before five shots, being more accentuated on fast surfaces [19,20].Another determining factor is the moment of impact with the ball, which is influenced by the place of the previous bounce, the type of stroke made, as well as the place where the shot is directed [21].These aspects have been studied independently, but not through a sequential analysis that could provide more effective information to improve training and subsequent performance in competition.
Based on the above, the aim of the research was to analyse the effectiveness in the achievement of the point using a system based on patterns of play with the most important performance indicators of tennis.If this is the goal of the study, the concept of patterns of play should be explained in the introduction.Furthermore, the authors should reference the studies that have previously used this concept in previous research.I am sure there are several studies that have analysed patterns of play in tennis.These papers should be mentioned.Which are the hypotheses tested in the study?The goal is mentioned, but the authors do not provide any hypotheses to be tested.This is crucial.

Method Design
Study to detect the effectiveness of playing patterns in professional men's tennis in which an observational methodology has been used [22].
The observational design [23] used is nomothetic (all points played in the final rounds of the Grand Slams in 2021 -from quarterfinals-, excluding the Australian Open), follow-up (one season), and unidimensional (there is no concurrence of behaviours).

Sample
Since the unit of analysis of this study is the points played in the different matches of the selected tournaments, a total of 4669 points were analysed (1660 at Roland Garros, 1623 at Wimbledon and 1386 at the US Open).All matches from the quarter-finals onwards were analysed, seven per tournament.The study was approved by the Ethics Committee of the Faculty of Education and Sport Science (University of Vigo, Application 02/0320).

Instruments
The observation instrument used for this study is the OBSTENNIS-v3, a system of categories that contemplates in its criteria the different possibilities of play in tennis.It is an adaptation of the OBSTENNIS-v2 [2].
The OBSTENNIS-v3 (table 1) is made up of seven criteria that form a system of categories that meets the conditions of exhaustiveness and mutual exclusivity.Data registration was performed with LINCE v.1.4software [24].

BOUNCE ZONE SZ
The point ends from the service zone (ace or double fault).

ZB1 to ZB5
The zone of the surface where the ball bounces before a winner or forced error (in this case the player who wins the point is registered).In the case of an unforced error, the bounce before the error is registered.In the case of a volley or smash, the area where the player's feet are placed is registered.

Z1 to Z5
Zone of the surface where the ball is finally directed (only for winners and forced errors).

NET
The final shot goes into the net or does not even reach the net.

LTO
The final shot goes out to the lateral side.

BSO
The final shot goes out on the baseline.

WINNER
SW The server wins the point.

RE
The returner wins the point.

SWW
The server wins with a winner.

SWFE
The server wins with a forced error.

SWUE
The server wins with a unforced error.

RWW
The returner wins a winner.

RWFE
The returner wins a forced error.

RWUE
The returner wins a unforced error.

SACE
The server wins with an ACE.

SWFH
The server wins with a forehand winner.

SWBH
The server wins with a backhand winner.

SWOT
The server wins with a winner with another type of stroke (drop shot, smash, volley...).

SFEFH
The server wins with a forehand by a forced error of the opponent.

SFEBH
The server wins with a backhand by a forced error of the opponent.

SFEOT
The server wins with another type of stroke by a forced error of the opponent.

SUEFH
The server wins with a forehand by an unforced error of the opponent.

SUEBH
The server wins with a backhand by an unforced error of the opponent.

SUEOT
The server wins with another type of stroke by an unforced error of the opponent.

RDF
The returner wins with an ACE RWFH The returner wins with a forehand winner RWBH The returner wins with a backhand winner RWOT The returner wins with a winner with another type of stroke (drop shot, smash, volley...).

RFEFH
The returner wins with a forehand by a forced error of the opponent.

RFEBH
The returner wins with a backhand by a forced error of the opponent.

RFEOT
The returner wins with another type of stroke by a forced error of the opponent.

RUEFH
The returner wins with a forehand by an unforced error of the opponent.

RUEBH
The returner wins with a backhand by an unforced error of the opponent.

RUEOT
The returner wins with another type of stroke by an unforced error of the opponent.After adequate training in the use of the instruments, the points were monitored and registered by two expert observers.To ensure rigour in the registration process [25], the quality of the registered data was controlled by calculating intra-and inter-observer agreement using the Kappa coefficient [26] calculated using LINCE software.Both concordances were performed on points that did not belong to the final sample (n=450; 1/10 of the final sample).

***
The intra-observer kappa was 0.93 for the first observer and 0.96 for the second observer.The inter-observer kappa was 0.94.
After the registration of all the points, we obtained an Excel file with the sequentiality of the behaviours.The versatility of this file allowed us to perform successive transformations for the different analyses [27].

Data Analysis
All statistical analyses were performed using IBM-Statistical Package for the Social Sciences, version 25.0 (IBM-SPSS Inc., Chicago, IL, USA).Statistical significance was assumed for p<0.05.
The χ2 test was used to contrast the differences between the categories of each criterion used (intra-criteria analysis), as well as to compare the differences between the playing surfaces (clay, grass or hard court) of Roland Garros, Wimbledon and US Open (inter-criteria analysis).
The analysis of the effectiveness of the playing sequences was carried out using the case selection technique combined with a frequency and cross-table analysis.
now the authors speak about behaviours…it seems not very clear…patterns, points, behaviours….itshould be clarified… now we talk about sequences….what is this?patterns, behaviours, points?

Descriptive statistical analysis
Table 2 shows the descriptive analysis of the study differentiated by type of surface, as well as the comparative analysis test between surfaces (χ2 inter-criteria).Statistically significant differences (p<0.05) were found between the categories of each of the criteria and on each of the three surfaces analysed (intra-criteria χ2).In the comparison between surfaces (inter-criteria χ2 test), statistically significant differences were observed in the type of rally (greater number of medium and long rallies on clay than on grass and hard court), the bounce zone (greater number of actions from zone 2 and fewer from the service on clay compared to the other surfaces), the final direction (among other aspects, fewer finishings with an around the net shot, more shots are sent to the lateral zone and to zone 5 on clay compared to other surfaces), the type of point resolution (on fast courts more points are won on serve due to a forced error by the opponent) and the type of final stroke (for more details see table S1 of the supplementary material).
The results show that first serve accuracy ranged from 65.1-61.8-63.6%depending on the surface (clay, grass or hard).Short rally points predominated (64.9-77.4-68.8%)although they were more frequent on fast surfaces.
Nearly half of the points analysed on the three surfaces ended after a bounce previous to the final shot into zone 1 (42.8-49.1-43%)and ended with a winner or forced error in zone 1 (24.1-32.9-33.2%).The points obtained (with a winner or forced error by the opponent) in zone 5 also stood out, especially on clay (11.4%).The surface where most points were won after the return was clay (37%), compared to 34.8% on grass and 35.3% on hard court.Both, serving and return, it is on clay where more winners were obtained (24.5% and 8% respectively; on grass 22.5% and 6.2% and on hard court 23.9% and 7%), although it is also the surface where not sure what is this played the finishing won fewer points were obtained by forced error serving (14.8% compared to 20.6% and 18.2%).An even amount of points won by returning (23.7-24.8-24.1%)and serving (23.6-22.1-22.7%)by unforced error was registered on all three surfaces.The surface with the most aces was hard court (11.2%) and the least on clay (6%).Unforced errors on the return had similar percentages after hitting with the forehand and backhand; however, when serving, they were much more frequent with the forehand.Winners are more frequent with the forehand, both serving and returning, and were considerably more frequent when serving.

Sequential analysis
Figure 2 shows a comparative analysis of the effectiveness of the point based on service, rally length and surface type.The effectiveness with the first serve was 69% on clay, 75% on grass and 75% on hard.
Second serve effectiveness was 55% on clay, 54% on grass and 57% on hard, a decrease in effectiveness of 14-21-18% respectively.Statistically significant differences were observed between surfaces in the first servicelong rally sequence (χ2=8.052;sig.=0.018).On both, grass and hard court, the returner was more effective in this type of pattern of play, but not on clay.
Figure 3 and figure 4 show an analysis, according to the type of surface and pattern of play (service and rally), of the distribution of points with respect to the type of resolution (winners, forced errors or unforced errors).

Do you mean analysis of patterns?
proportion of the total.The points won by serving through an unforced error by the opponent are usually sent to the net (59%).Most of the points won by the returner are by unforced error with a shot to the net (59%).On hard court, the data was similar to that on grass, with a high number of forced errors (46%) sent to zone 1 (93%).Winners (16%) were mostly directed to zone 1 (44%) but there were shots sent to all other zones (around 15%).
In Supplementary Material Table S3 an analysis of patterns of play was carried out taking into account the type of surface, the service and the rally as a function of the way of resolution and the final stroke (forehand, backhand or other stroke).
On clay, winners when the player served were more frequent with the forehand than with the backhand in all the possible match situations studied, something that did not occur on grass or hard court.Returning, winners were predominantly with the forehand on clay and hard court, but on grass, many points were resolved with another type of stroke (probably volleys).
Unforced error points won on serve were very even on clay with first serves (regardless of the type of rally) and second serves in short rallies.On grass and hard courts, this balance was only evident with first serves in short and medium rallies.In all other cases, forehand errors predominated, except in short rallies in second serves on hard courts.
The points won by unforced errors on grass when the player was returning was linked to a forehand (occurred in all possible solutions).On clay it was the same in short rallies (both first and second serves), there was a balance between forehand and backhand errors in medium rallies and in long rallies the error was preceded by a backhand stroke.On the hard surface, there was a balance of forehand and backhand errors in almost all the situations analysed, except for the first serve and short rallies, where the errors were clearly caused by a forehand.
to more aggressive playing strategies by players, where they put pressure on the opponent from the very beginning [32][33][34].Furthermore, it has also been shown that players who dominated short rallies (0-4 strokes) won the match in 9 out of 10 cases, both on clay and grass [15,20], hence tactical trainings should try to optimise this aspect of the game.The best strategy for the player serving with a first serve and short rally was to look for a winner, as 34-36% of the cases obtained the point later on either surface.In addition, especially on grass, a high percentage of forced errors by the opponent was registered (32%), dropping to 27% on hard and 20% on clay.
The best return strategy was to look for an unforced error from the opponent, regardless of the surface, although this was more effective on clay (17%) than on grass (15%) or hard court (13%).Return winners after the first serve were rather scarce in short rallies (3-4%).With this information, and considering that the returner is probably always at a tactical disadvantage [12], training to work on the defence of the serve should be aimed at trying to put the server in a situation of discomfort, rather than trying to find a winner, at least until after four rallies.Hitting the ball to zone 3 (baseline) and zone 4 (backhand on the right-handed player) were the most effective, confirming that the search for the opponent's error occurs more frequently on the backhand stroke [21].
Medium rally points represented 21.6-15.7-18.0% in this study depending on the surface.According to one study [20], dominance on these points determines the winner of a clay court match by 65% and 69% on grass (approximately 25% less than dominance on short rallies).With the first serve, the tactic of looking for a winner on either surface was not more effective, but rather the search for an unforced error from the opponent.When returning the serve the same happened.The points won by unforced error were very balanced between server and returner, so it seems clear that, at a strategic level, the server is not interested in reaching this type of rally [35].This highlights the importance of having an effective service to end the point as soon as possible and thus improve the probability of success at the point [12,30,35,36].
With the second serve, the statistics do not vary much with respect to the first serve, except that the points won by unforced errors on hard courts increase (+16.6%).This would suggest that the effect of the serve is diluted after the fifth shot, something that has already been suggested in the literature [35] On clay, with this rally and second serve, the tactic of looking for a winner (winner or forced error) was more effective than looking for the unforced error.In the return game, the opposite was true.On grass it was more effective to look for the unforced error both on serve and return.On hard courts it was much more effective to look for the unforced error, especially in the return.
Long rally points were few in general, although this fact was more pronounced on grass, where not even 7% were observed.Although it was not investigated whether these points were important points (e.g.: breakpoints), the literature has pointed out that dominance on these types of points is linked to match success in 66% of cases on clay and 61% on grass [15], quite similar to that of medium rallies, so they must also have their importance in training, both from a physical, psychological and strategic point of view.In fact, there is a curious fact, at least on fast surfaces.The server won fewer points after a first serve than the returner, but significantly increased his effectiveness with a second serve.The explanation for this phenomenon is complex, but it may possibly be linked to aspects of concentration, due to starting from a disadvantageous situation (second serve).

Practical application
Throughout this article, different guidelines have been established for patterns of effectiveness depending on the service, surface and rally.In any case, we recommend that coaches make use of the different tables and figures in the manuscript, as well as the supplementary material to obtain more specific data, where an analysis is also made according to the bounce zone prior to the last shot, type of final stroke and direction of the final shot, all differentiated by surface, type of service and rally length.

Limitations and future perspectives
In this study we have only analysed matches from the Grand Slam quarter-finals onwards, so previous rounds have not been taken into account.The direction of the serve (wide, body or T zone) and its speed have not been considered, aspects that could be interesting to address in future research.
Bearing in mind that most of the points end in short rallies (0-4 shots), in the future studies should be carried out linked to the exact number of shots in the point, focusing on this type of rally, in order to establish more specific patterns of effectiveness, taking into account all the movements and strokes made by the players.

Conclusions
The first serve is essential for the effectiveness on all types of rally and surfaces.Starting the point on the second serve decreases the effectiveness by 14.6% (clay), 21% (grass) or 17% (hard court) compared to the first serve.The probability of winning the point with a first serve and medium rally decreases by 25-29% depending on the surface compared to finishing with a short rally.On grass only 7% of points end with a long rally (13% on the other two surfaces).
The most repeated pattern of play and the most effective for the server was the start of the point with a first serve with a final shot after a bounce in the service zone (zone 1) after a rally of less than five shots.This generated an unforced error in the opponent (on clay) or a forced error (on grass and hard court).
Funded studies Enter a statement with the following details: Initials of the authors who received each award • Grant numbers awarded to each author • The full name of each funder • URL of each funder website • Did the sponsors or funders play any role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript?• NO -Include this sentence at the end of your statement: The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.• YES -Specify the role(s) played.• * typeset Competing Interests Use the instructions below to enter a competing interest statement for this submission.On behalf of all authors, disclose any competing interests that could be perceived to bias this work-acknowledging all financial support and any other relevant financial or nonfinancial competing interests.This statement is required for submission and will appear in the published article if the submission is accepted.Please make sure it is accurate and that any funding sources listed in your Funding Information later in the submission form are also declared in your Financial Disclosure statement.View published research articles from PLOS ONE for specific examples.The authors have declared that no competing interests exist.NO authors have competing interests Enter: The authors have declared that no competing interests exist.Authors with competing interests Enter competing interest details beginning with this statement: I have read the journal's policy and the authors of this manuscript have the following competing interests: [insert competing interests here] * typeset Ethics Statement Enter an ethics statement for this submission.This statement is required if the study involved: /A" if the submission does not require an ethics statement.General guidance is provided below.Consult the submission guidelines for detailed instructions.Make sure that all information entered here is included in the Methods section of the manuscript.N/A Powered by Editorial Manager® and ProduXion Manager® from Aries Systems Corporation Format for specific study types Human Subject Research (involving human participants and/or tissue) Give the name of the institutional review board or ethics committee that approved the study • Include the approval number and/or a statement indicating approval of this research • Indicate the form of consent obtained (written/oral) or the reason that consent was not obtained (e.g. the data were analyzed anonymously) • Animal Research (involving vertebrate animals, embryos or tissues) Provide the name of the Institutional Animal Care and Use Committee (IACUC) or other relevant ethics board that reviewed the study protocol, and indicate whether they approved this research or granted a formal waiver of ethical approval • Include an approval number if one was obtained • If the study involved non-human primates, add additional details about animal welfare and steps taken to ameliorate suffering • If anesthesia, euthanasia, or any kind of animal sacrifice is part of the study, include briefly which substances and/or methods were applied • Field Research Include the following details if this study involves the collection of plant, animal, or other materials from a natural setting: Field permit number • Name of the institution or relevant body that granted permission • Data Availability Authors are required to make all data underlying the findings described fully available, without restriction, and from the time of publication.PLOS allows rare exceptions to address legal and ethical concerns.See the PLOS Data Policy and FAQ for detailed information.

Figure 1
carried out by recording the matches of three out of the four Grand Slams of the 2021 season (one on each surface).

Figure 4
Figure 4 Powered by Editorial Manager® and ProduXion Manager® from Aries Systems CorporationPowered by Editorial Manager® and ProduXion Manager® from Aries Systems Corporation

Table 2 .
Distribution of points on the different surfaces in the 2021 season and comparative analysis between surfaces (χ2 inter-criteria)